Orthant probabilities and the attainment of maxima on a vertex of a simplex

Abstract

We calculate bounds for orthant probabilities for the equicorrelated multivariate normal distribution and use these bounds to show the following: for degree k>4, the probability that a k-homogeneous polynomial in n variables attains a local constrained maximum on a vertex of the n-dimensional simplex tends to one as the dimension n grows. The bounds we obtain for the orthant probabilities are tight up to log⁡(n) factors.Fil: Pinasco, Damian. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Torcuato Di Tella; ArgentinaFil: Smucler, Ezequiel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Torcuato Di Tella; ArgentinaFil: Zalduendo, Ignacio Martin. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Torcuato Di Tella; Argentin

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